The fact that the Earth is not flat, people have known for a long time. Ancient navigators observed how the picture of the starry sky gradually changes: new constellations become visible, while others, on the contrary, go beyond the horizon. Ships sailing away into the distance "go under water", the last to disappear from view are the tops of their masts. Who first proposed the idea of the sphericity of the Earth is unknown. Most likely - the Pythagoreans, who considered the ball the most perfect of the figures. A century and a half later, Aristotle gives several proofs that the Earth is a sphere. The main one: during a lunar eclipse, the shadow from the Earth is clearly visible on the surface of the Moon, and this shadow is round! Since then, attempts have been constantly made to measure the radius of the globe. Two simple methods are described in exercises 1 and 2. The measurements, however, were inaccurate. Aristotle, for example, was wrong by more than one and a half times. It is believed that the first who managed to do this with high accuracy was the Greek mathematician Eratosthenes of Cyrene (276-194 BC). His name is now known to all thanks to sieve of Eratosthenes a way to find prime numbers (Fig. 1).
Rice. one |
If you cross out one from the natural series, then cross out all even numbers except the first one (the number 2 itself), then all numbers that are multiples of three, except for the first of them (number 3), etc., then as a result there will be only prime numbers . Eratosthenes was famous among his contemporaries as the greatest scientist and encyclopedist, who was engaged not only in mathematics, but also in geography, cartography and astronomy. For a long time he headed the Library of Alexandria, the center of world science of that time. Working on the compilation of the first atlas of the Earth (of course, it was about the part known by that time), he decided to make an accurate measurement of the globe. The idea was this. In Alexandria, everyone knew that in the south, in the city of Siena (modern Aswan), one day a year, at noon, the Sun reaches its zenith. The shadow from the vertical pole disappears, the bottom of the well is illuminated for several minutes. This happens on the day of the summer solstice, June 22 - the day of the highest position of the Sun in the sky. Eratosthenes sends his assistants to Siena, and they establish that at exactly noon (according to the sundial) the Sun is exactly at its zenith. At the same time (as it is written in the original source: “at the same hour”), i.e. at noon according to the sundial, Eratosthenes measures the length of the shadow from the vertical pole in Alexandria. It turned out a triangle ABC (AC- six, AB- shadow, fig. 2).
So, a ray of sunshine in Siena ( N) is perpendicular to the surface of the Earth, and therefore passes through its center - the point Z. A beam parallel to it in Alexandria ( BUT) makes an angle γ = ACB with vertical. Using the equality of cross-lying angles at parallel ones, we conclude that AZN= γ. If denoted by l circumference, and through X the length of its arc AN, then we get the proportion . Angle γ in a triangle ABC Eratosthenes measured, it turned out 7.2 °. Value X - nothing more than the length of the path from Alexandria to Siena, about 800 km. Eratosthenes accurately calculates it, based on the average travel time of camel caravans that regularly traveled between the two cities, as well as using data Bematists - people of a special profession who measured distances with steps. Now it remains to solve the proportion, getting the circumference (i.e., the length of the earth's meridian) l= 40000 km. Then the radius of the earth R equals l/(2π), this is approximately 6400 km. The fact that the length of the earth's meridian is expressed as such a round number of 40,000 km is not surprising if we recall that the unit of length of 1 meter was introduced (in France at the end of the 18th century) as one forty-millionth part of the Earth's circumference (by definition!). Eratosthenes, of course, used a different unit of measure - stages(about 200 m). There were several stages: Egyptian, Greek, Babylonian, and which of them Eratosthenes used is unknown. Therefore, it is difficult to judge for sure about the accuracy of its measurement. In addition, an inevitable error arose due to the geographical location of the two cities. Eratosthenes reasoned as follows: if the cities are on the same meridian (i.e., Alexandria is located exactly north of Syene), then noon occurs in them at the same time. Therefore, by making measurements at the time of the highest position of the Sun in each city, we should get the correct result. But in fact, Alexandria and Siena are far from being on the same meridian. Now it is easy to verify this by looking at the map, but Eratosthenes did not have such an opportunity, he just worked on compiling the first maps. Therefore, his method (absolutely correct!) led to an error in determining the radius of the Earth. However, many researchers are confident that the accuracy of Eratosthenes' measurement was high and that he was wrong by less than 2%. Humanity was able to improve this result only after 2 thousand years, in the middle of the 19th century. A group of scientists in France and the expedition of V. Ya. Struve in Russia worked on this. Even in the era of great geographical discoveries, in the 16th century, people could not achieve the result of Eratosthenes and used the incorrect value of the earth's circumference of 37,000 km. Neither Columbus nor Magellan knew what the true dimensions of the Earth were and what distances they would have to overcome. They thought that the length of the equator was 3,000 km less than it actually was. If they had known, they might not have swum.
What is the reason for such a high accuracy of the method of Eratosthenes (of course, if he used the right stage)? Before him, the measurements were local, on the distances visible to the human eye, i.e. no more than 100 km. These are, for example, the methods in exercises 1 and 2. In this case, errors are inevitable due to the terrain, atmospheric phenomena, etc. To achieve greater accuracy, you need to take measurements globally, at distances comparable to the radius of the Earth. The distance of 800 km between Alexandria and Siena turned out to be quite sufficient.
How the Moon and the Sun were measured. Three steps of Aristarchus
The Greek island of Samos in the Aegean is now a remote province. Forty kilometers long, eight kilometers wide. Three of the greatest geniuses were born on this tiny island at different times - the mathematician Pythagoras, the philosopher Epicurus and the astronomer Aristarchus. Little is known about the life of Aristarchus of Samos. Dates of life are approximate: born about 310 BC, died about 230 BC. We don’t know what he looked like, not a single image has survived (the modern monument to Aristarchus in the Greek city of Thessaloniki is just a sculptor’s fantasy). He spent many years in Alexandria, where he worked in the library and in the observatory. His main achievement - the book "On the magnitudes and distances of the Sun and Moon", - according to the unanimous opinion of historians, is a real scientific feat. In it, he calculates the radius of the Sun, the radius of the Moon, and the distances from the Earth to the Moon and to the Sun. He did it alone, using very simple geometry and the well-known results of observations of the Sun and Moon. Aristarchus does not stop at this, he makes several important conclusions about the structure of the Universe, which are far ahead of their time. It is no coincidence that he was subsequently called the "Copernicus of antiquity."
The calculation of Aristarchus can be conditionally divided into three steps. Each step is reduced to a simple geometric problem. The first two steps are quite elementary, the third is a little more complicated. In geometric constructions, we will denote by Z, S and L centers of the Earth, Sun and Moon, respectively, and through R, Rs and Rl are their radii. We will consider all celestial bodies as balls, and their orbits as circles, as Aristarchus himself considered (although, as we now know, this is not entirely true). We start with the first step, and for this we will observe the moon a little.
Step 1. How many times further away is the Sun than the Moon?
As you know, the moon shines by reflected sunlight. If you take a ball and shine on it from the side with a large spotlight, then in any position exactly half of the surface of the ball will be illuminated. The boundary of the illuminated hemisphere is a circle lying in a plane perpendicular to the rays of light. Thus, the Sun always illuminates exactly half of the surface of the Moon. The shape of the moon that we see depends on how this illuminated half is located. At new moon When the Moon is not visible at all in the sky, the Sun illuminates its far side. Then the illuminated hemisphere gradually turns towards the Earth. We begin to see a thin crescent, then a month (“growing moon”), then a semicircle (this phase of the moon is called “squaring”). Then, day by day (or rather, night by night), the semicircle grows to the full moon. Then the reverse process begins: the illuminated hemisphere turns away from us. The moon "gets old", gradually turning into a month, turned to us with its left side, like the letter "C", and, finally, disappears on the night of the new moon. The period from one new moon to the next lasts approximately four weeks. During this time, the Moon makes a complete revolution around the Earth. From the new moon to half the moon, a quarter of the period passes, hence the name "squaring".
Aristarchus' remarkable conjecture was that, when quadrature, the sun's rays illuminating half of the Moon are perpendicular to the straight line connecting the Moon to the Earth. So in a triangle ZLS apex angle L- straight (Fig. 3). If we now measure the angle LZS, denote it by α, then we get that = cos α. For simplicity, we assume that the observer is at the center of the Earth. This will not greatly affect the result, since the distances from the Earth to the Moon and to the Sun are much greater than the radius of the Earth. So, having measured the angle α between the rays ZL and ZS during the quadrature, Aristarchus calculates the ratio of the distances to the Moon and to the Sun. How to simultaneously catch the Sun and the Moon in the sky? This can be done early in the morning. The difficulty arises for another, unexpected reason. In the time of Aristarchus, there were no cosines. The first concepts of trigonometry will appear later, in the works of Apollonius and Archimedes. But Aristarchus knew what similar triangles were, and that was enough. Drawing a small right triangle Z"L"S" with the same acute angle α = L"Z"S" and measuring its sides, we find that , and this ratio is approximately equal to 1/400.
Step 2. How many times larger is the Sun than the Moon?
In order to find the ratio of the radii of the Sun and the Moon, Aristarchus uses solar eclipses (Fig. 4). They occur when the moon blocks the sun. With partial, or, as astronomers say, private, during an eclipse, the Moon only passes over the disk of the Sun, without completely covering it. Sometimes such an eclipse cannot even be seen with the naked eye, the Sun shines like on a normal day. Only through a strong darkening, for example, smoked glass, one can see how part of the solar disk is covered by a black circle. Much less often, a total eclipse occurs when the Moon completely covers the solar disk for several minutes.
At this time, it becomes dark, stars appear in the sky. Eclipses terrified ancient people, were considered harbingers of tragedies. A solar eclipse is observed in different ways in different parts of the Earth. During a total eclipse, a shadow from the Moon appears on the surface of the Earth - a circle whose diameter does not exceed 270 km. Only in those regions of the globe through which this shadow passes, a total eclipse can be observed. Therefore, in the same place, a total eclipse occurs extremely rarely - on average, once every 200-300 years. Aristarchus was lucky - he was able to observe a total solar eclipse with his own eyes. In a cloudless sky, the Sun gradually began to dim and decrease in size, twilight set in. For a few moments the sun disappeared. Then the first ray of light appeared, the solar disk began to grow, and soon the Sun shone in full force. Why does the eclipse last for such a short time? Aristarchus replies: the reason is that the Moon has the same apparent dimensions in the sky as the Sun. What does it mean? Let's draw a plane through the centers of the Earth, the Sun and the Moon. The resulting section is shown in Figure 5 a. Angle between tangents drawn from a point Z to the circumference of the moon is called angular size the moon, or her angular diameter. The angular size of the Sun is also determined. If the angular diameters of the Sun and the Moon are the same, then they have the same apparent size in the sky, and during an eclipse, the Moon really completely blocks the Sun (Fig. 5 b), but only for a moment, when the rays coincide ZL and ZS. The photograph of a total solar eclipse (see Fig. 4) clearly shows the equality of sizes.
The conclusion of Aristarchus turned out to be amazingly accurate! In reality, the average angular diameters of the Sun and the Moon differ by only 1.5%. We are forced to talk about average diameters, since they change during the year, since the planets do not move in circles, but in ellipses.
Connecting the center of the earth Z with the centers of the sun S and moon L, as well as with touch points R and Q, we get two right triangles ZSP and ZLQ(see fig. 5 a). They are similar because they have a pair of equal acute angles β/2. Consequently, . In this way, the ratio of the radii of the Sun and the Moon is equal to the ratio of the distances from their centers to the center of the Earth. So, Rs/Rl= κ = 400. Despite the fact that their apparent sizes are equal, the Sun turned out to be 400 times larger than the Moon!
The equality of the angular sizes of the Moon and the Sun is a happy coincidence. It does not follow from the laws of mechanics. Many planets in the solar system have satellites: Mars has two, Jupiter has four (and several dozen smaller ones), and they all have different angular sizes that do not coincide with the solar one.
Now we proceed to the decisive and most difficult step.
Step 3. Calculating the sizes of the Sun and Moon and their distances
So, we know the ratio of the sizes of the Sun and the Moon and the ratio of their distances to the Earth. This information relative: it restores the picture of the surrounding world only up to similarity. You can remove the Moon and the Sun from the Earth 10 times, increasing their size by the same factor, and the picture visible from the Earth will remain the same. To find the real sizes of celestial bodies, it is necessary to correlate them with some known size. But of all the astronomical quantities, Aristarchus still knows only the radius of the globe R= 6400 km. Will it help? Does the radius of the Earth appear in any of the visible phenomena occurring in the sky? It is no coincidence that they say "heaven and earth", meaning two incompatible things. And yet such a phenomenon exists. This is a lunar eclipse. With its help, using a rather ingenious geometric construction, Aristarchus calculates the ratio of the radius of the Sun to the radius of the Earth, and the circuit closes: now we simultaneously find the radius of the Moon, the radius of the Sun, and at the same time the distances from the Moon and from the Sun to the Earth.
Comparing the circles of the Earth's shadow on the Moon during a lunar eclipse, Aristarchus found the numbert= 8/3 is the ratio of the radius of the Earth's shadow to the radius of the Moon. In addition, he has already calculated κ = 400 (the ratio of the radius of the Sun to the radius of the Moon, which is almost equal to the ratio of the Sun-Earth distance to the Moon-Earth distance). After rather non-trivial geometric constructions, Aristarchus finds that the ratio of the diameters of the Sun and the Earth is , and the Moon and the Earth is . Substituting the known quantities κ = 400 and t= 8/3, we get that the Moon is approximately 3.66 times smaller than the Earth, and the Sun is 109 times larger than the Earth. Since the radius of the earth R we know, we find the radius of the moon Rl= R/3.66 and the radius of the Sun Rs= 109R.
Now the distances from the Earth to the Moon and to the Sun are calculated in one step, this can be done using the angular diameter. The angular diameter β of the Sun and Moon is about half a degree (0.53° to be exact). How the ancient astronomers measured it, we will talk about this ahead. Dropping the tangent ZQ on the circumference of the moon, we get a right triangle ZLQ with an acute angle β/2 (Fig. 10).
From it we find that is approximately equal to 215 Rl, or 62 R. Similarly, the distance to the Sun is 215 Rs = 23 455R.
Everything. The sizes of the Sun and the Moon and the distances to them are found.
About the benefits of mistakes
In fact, everything was somewhat more complicated. Geometry was just being formed, and many things familiar to us since the eighth grade of school were not at all obvious at that time. It took Aristarchus to write a whole book to present what we have presented in three pages. And with experimental measurements, too, everything was not easy. First, Aristarchus made a mistake in measuring the diameter of the earth's shadow during a lunar eclipse, obtaining the ratio t= 2 instead of . In addition, he seemed to proceed from the wrong value of the angle β - the angular diameter of the Sun, assuming it to be 2°. But this version is controversial: Archimedes in his treatise "Psammit" writes that, on the contrary, Aristarchus used the almost correct value of 0.5 °. However, the most terrible mistake occurred at the first step, when calculating the parameter κ - the ratio of the distances from the Earth to the Sun and to the Moon. Instead of κ = 400, Aristarchus got κ = 19. How could it be more than 20 times wrong? Let us turn again to step 1, Figure 3. In order to find the ratio κ = ZS/ZL, Aristarchus measured the angle α = SZL, and then κ = 1/cos α. For example, if the angle α were equal to 60°, then we would get κ = 2, and the Sun would be twice as far from the Earth as the Moon. But the result of the measurement turned out to be unexpected: the angle α turned out to be almost right. This meant that the leg ZS many times superior ZL. Aristarchus got α = 87°, and then cos α = 1/19 (recall that all our calculations are approximate). The true value of the angle , and cos α =1/400. So a measurement error of less than 3° led to an error of 20 times! Having completed the calculations, Aristarchus comes to the conclusion that the radius of the Sun is 6.5 radii of the Earth (instead of 109).
Mistakes were inevitable given the imperfect measuring instruments of the day. More importantly, the method turned out to be correct. Soon (by historical standards, that is, after about 100 years), the outstanding astronomer of antiquity Hipparchus (190 - ca. 120 BC) will eliminate all inaccuracies and, following the method of Aristarchus, calculate the correct sizes of the Sun and Moon. Perhaps the error of Aristarchus turned out to be even useful in the end. Before him, the prevailing opinion was that the Sun and the Moon either have the same size (as it seems to an earthly observer), or differ slightly. Even the 19 times difference surprised contemporaries. Therefore, it is possible that if Aristarchus had found the correct ratio κ = 400, no one would have believed in it, and perhaps the scientist himself would have abandoned his method, considering the result absurd. .. For 17 centuries before Copernicus, he realized that the center of the world is not the Earth, but the Sun. Thus, for the first time, the heliocentric model and the concept of the solar system appeared.
What's in the center?
The idea of the structure of the Universe that prevailed in the Ancient World, familiar to us from the lessons of history, was that in the center of the world there is a motionless Earth, 7 planets revolve around it in circular orbits, including the Moon and the Sun (which was also considered a planet). It ends with a celestial sphere with stars attached to it. The sphere revolves around the Earth, making a complete revolution in 24 hours. Over the years, this model has been amended many times. So, they began to believe that the celestial sphere is motionless, and the Earth rotates around its axis. Then they began to correct the trajectories of the planets: the circles were replaced by cycloids, that is, lines that describe the points of the circle as it moves along another circle (you can read about these wonderful lines in the books of G. N. Berman "Cycloid", A. I. Markushevich "Remarkable curves", as well as in "Quantum": article by S. Verov "Secrets of the cycloid" No. 8, 1975, and article by S. G. Gindikin "Star Age of the cycloid", No. 6, 1985). Cycloids were in better agreement with the results of observations, in particular, they explained the "backwards" motions of the planets. It - geocentric system of the world, in the center of which is the Earth ("gay"). In the II century, it took its final form in the book "Almagest" by Claudius Ptolemy (87-165), an outstanding Greek astronomer, namesake of the Egyptian kings. Over time, some cycloids became more complicated, more and more new intermediate circles were added. But on the whole, the Ptolemaic system dominated for about one and a half millennia, until the 16th century, before the discoveries of Copernicus and Kepler. At first, Aristarchus also adhered to the geocentric model. However, after calculating that the radius of the Sun was 6.5 times that of the Earth, he asked a simple question: why should such a large Sun revolve around such a small Earth? After all, if the radius of the Sun is 6.5 times greater, then its volume is almost 275 times greater! This means that the Sun must be at the center of the world. 6 planets revolve around it, including the Earth. And the seventh planet, the Moon, revolves around the Earth. So there was heliocentric system of the world ("helios" - the Sun). Already Aristarchus himself noted that such a model better explains the apparent motion of the planets in circular orbits, and is in better agreement with the results of observations. But neither scientists nor official authorities accepted it. Aristarchus was accused of godlessness and was persecuted. Of all the astronomers of antiquity, only Seleucus became a supporter of the new model. No one else accepted it, at least historians do not have solid information on this matter. Even Archimedes and Hipparchus, who revered Aristarchus and developed many of his ideas, did not dare to place the Sun at the center of the world. Why?
Why didn't the world adopt the heliocentric system?
How did it happen that for 17 centuries scientists did not accept the simple and logical system of the world proposed by Aristarchus? And this despite the fact that the officially recognized geocentric system of Ptolemy often failed, not being consistent with the results of observations of the planets and stars. I had to add more and more new circles (the so-called nested loops) for the "correct" description of the motion of the planets. Ptolemy himself was not afraid of difficulties, he wrote: “Why be surprised at the complex movement of celestial bodies if their essence is unknown to us?” However, by the XIII century, these circles had accumulated 75! The model became so cumbersome that cautious objections began to be heard: is the world really so complicated? The case of Alphonse X (1226-1284), king of Castile and Leon, a state that occupied part of modern Spain, is widely known. He, the patron of sciences and arts, who gathered at his court fifty of the best astronomers in the world, said at one of the scientific conversations that “if the Lord had honored me and asked my advice during the creation of the world, much would have been arranged more simply.” Such insolence was not forgiven even to kings: Alphonse was deposed and sent to a monastery. But doubts remained. Some of them could be resolved by placing the Sun at the center of the Universe and adopting the system of Aristarchus. His works were well known. However, for many centuries, none of the scientists dared to take such a step. The reasons were not only in fear of the authorities and the official church, which considered Ptolemy's theory to be the only true one. And not only in the inertia of human thinking: it is not so easy to admit that our Earth is not the center of the world, but just an ordinary planet. Still, for a real scientist, neither fear nor stereotypes are obstacles on the way to the truth. The heliocentric system was rejected for quite scientific, one might even say, geometrical reasons. If we assume that the Earth revolves around the Sun, then its trajectory is a circle with a radius equal to the distance from the Earth to the Sun. As we know, this distance is equal to 23,455 Earth radii, i.e., more than 150 million kilometers. This means that the Earth moves 300 million kilometers in half a year. Giant size! But the picture of the starry sky for the earthly observer remains the same. The Earth is either approaching or moving away from the stars by 300 million kilometers, but neither the apparent distances between the stars (for example, the shape of the constellations) nor their brightness change. This means that the distances to the stars must be several thousand times greater, i.e., the celestial sphere must have completely unimaginable dimensions! This, by the way, was realized by Aristarchus himself, who wrote in his book: “The volume of the sphere of fixed stars is so many times greater than the volume of a sphere with an Earth-Sun radius, how many times the volume of the latter is greater than the volume of the globe”, i.e. according to Aristarchus it turned out that the distance to the stars is (23 455) 2 R, this is more than 3.5 trillion kilometers. In reality, the distance from the Sun to the nearest star is still about 11 times greater. (In the model that we presented at the very beginning, when the distance from the Earth to the Sun is 10 m, the distance to the nearest star is ... 2700 kilometers!) Instead of a compact and cozy world, in the center of which the Earth is located and which is placed inside a relatively small celestial sphere, Aristarchus drew the abyss. And this abyss frightened everyone.
The sun is the central object of our star system. Almost all of its mass is concentrated in it - 99%. You can determine the size of a celestial body using observation, geometric models and accurate calculations. Scientists need not only to know the diameter of the Sun in kilometers, as well as its angular dimensions, but also to track the activity of the star. Its influence on our planet is very great - streams of charged particles strongly affect the Earth's magnetosphere.
How to determine the diameter of the Sun in kilometers
Determining the diameter of the Sun has always occupied people interested in astronomy. Since ancient times, man has been observing the sky and trying to get an idea of the objects visible on it. With their help, calendars were created and many natural phenomena were predicted. Heavenly bodies have been given mystical significance for thousands of years.
The Moon and the Sun became the central objects of study. With the help of the Earth's satellite, it was possible to find out the exact dimensions of the star. The diameter of the Sun was determined using the Bailey Rosary. This is the name of the optical effect that occurs during the phase of a total solar eclipse. When the edges of the solar and lunar disks coincide, light breaks through the irregularities of the lunar surface, forming red dots. They helped astronomers determine the exact position of the edge of the solar disk.
The most detailed studies of this phenomenon were carried out in Japan in 2015. Data from several observatories were supplemented with information from the Kaguya lunar probe. As a result, it was calculated how much the diameter of the Sun is in kilometers - 1 million 392 thousand 20 km. Other parameters of the star are also important for astronomers.
Angular diameter of the Sun
The angular diameter of an object is the angle between lines extending from the observer to diametrically opposite points on its edges. In astronomy, it is measured in minutes (′) and seconds (″). By it is meant not a flat angle, but a solid one (the union of all rays emerging from a point). The angular diameter of the star is 31′59″.
During the day, the Sun changes its size (2.5-3.5 times). However, this appearance is only a psychological phenomenon. The illusion of perception lies in the fact that the angle at which the Sun is seen does not change depending on its position in the sky.
However, the sky appears to a person not as a hemisphere, but as a dome, which adjoins the horizon along the edges. Therefore, the projection of the star onto its plane seems to be different in magnitude.
There is another explanation. All objects become smaller as they approach the horizon. However, the Sun does not change its size. This makes it look like it's getting bigger. An interesting psychological effect is easy to check: it is worth measuring the diameter of the Sun with the help of the little finger. Its dimensions at the zenith and on the horizon will be the same.
Solar research
Before the invention of the telescope, astronomers had no idea about the structure of the heavenly body. In Europe, sunspots were discovered only in the 17th century. They are magnetic fields escaping to the surface of the photosphere. Interfering with the movement of matter in places of ejection, they create a decrease in temperature on the surface of the Sun. At the same time, Galileo determined the period of revolution of the Sun around its axis. Its outer layer makes a complete revolution in 25.38 days.
Structure of the Sun:
- hydrogen - 70%;
- helium - 28%;
- other elements - 2%.
In the core of a star, a nuclear reaction takes place, converting hydrogen into helium. Here the temperature reaches 15 billion degrees. On the surface, it is equal to 5780 degrees.
After the advent of spacecraft, many attempts were made to study the celestial body. American satellites launched into space between 1962 and 1975 studied the Sun in the ultraviolet and X-ray wavelengths. The series was named the Orbital Solar Observatory.
In 1976, the West German satellite KA Helios-2 was launched, which approached the star at a distance of 43.4 million km. It was intended to study the solar wind. With the same purpose, in 1990, the Ulysses Solar Probe went into outer space.
NASA plans to launch the Solar Probe Plus satellite in 2018, which will approach the Sun by 6 million kilometers. Such a distance will be a record for the last decades.
Comparison with other celestial bodies
When determining the size of the Sun, comparison with other celestial objects helps. Interesting perspective comparison. For example, the diameter of the Sun is 109 Earth diameters, 9.7 Jupiter diameters. Gravity on the Sun exceeds Earth's gravity by 28 times. A person here would weigh 2 tons.
The mass of the star is 333 thousand Earth masses. The polar star is 30 times larger than the sun. Among the heavenly bodies, it has an average size. The Sun is still far from the giants. The largest star VY Canis Majoris has 2100 solar diameters.
Impact on the Earth
Life on Earth is possible only at a distance of 149.6 million km. from the sun. All living organisms receive the necessary heat from it, and photosynthesis is carried out by plants only with the participation of light. Thanks to this star, weather phenomena such as wind, rain, seasons, etc. are possible.
The answer to the question of what diameter of the Sun is needed for the normal development of life on a planet like Earth is simple - exactly the same as it is now. Our planet's magnetic field often reflects "solar wind attacks". Thanks to him, the northern and southern lights appear at the poles. During the period of solar flares, it can appear even near the equator.
The influence of the luminary on the climate of our planet is also significant. The period from 1683 to 1989 had the coldest winters. This was due to a decrease in the activity of the star.
A look into the future
The diameter of the Sun is changing. In 5 billion years it will have used up all its hydrogen fuel and become a red giant. Having increased in size, it will absorb Mercury and Venus. Then the Sun will shrink to the size of the Earth, turning into a white dwarf star.
The size of the star that determines life on our planet is one of the most interesting data not only for scientists, but also for ordinary people. The development of astronomy makes it possible to determine the distant future of celestial bodies and contributes to the accumulation of information for the meteorological service. The development of new planets also becomes possible, the level of protection of the Earth from collisions with small celestial bodies increases.
The Sun is a star whose surface temperature reaches several thousand degrees, so its light, even after traveling a great distance from the Earth, remains too bright for the Sun to be seen with the naked eye.Therefore, it is rather difficult for an ordinary person to estimate the size and shape of the Sun. At the same time, astronomers have established that the Sun is a ball that has an almost regular shape. Therefore, to estimate the size of the Sun, you can use the standard indicators used to measure the size of a circle.
Thus, the diameter of the Sun is 1.392 million kilometers. For comparison, the diameter of the Earth is only 12,742 kilometers: thus, according to this indicator, the size of the Sun exceeds the size of our planet by 109 times. At the same time, the circumference of the Sun along the equator reaches 4.37 million kilometers, while for the Earth this figure is only 40,000 kilometers, in this dimension the dimensions of the Sun are larger than the dimensions of our planet, by the same number of times.
However, due to the huge temperature on the surface of the Sun, which is almost 6 thousand degrees, its size is gradually decreasing. Scientists who study solar activity claim that the Sun shrinks by 1 meter in diameter every hour. Thus, they suggest, a hundred years ago, the diameter of the Sun was approximately 870 kilometers larger than at present.
mass of the sun
The mass of the Sun differs from the mass of the planet Earth even more significantly. So, according to astronomers, at the moment the mass of the Sun is about 1.9891 * 10 ^ 30 kilograms. In this case, the mass of the Earth is only 5.9726 * 10 ^ 24 kilograms. Thus, the Sun is heavier than the Earth by almost 333 thousand times.At the same time, due to the high temperature on the surface of the Sun, most of its constituent substances are in a gaseous state, which means they have a fairly low density. So, 73% of the composition of this star is hydrogen, and the rest is helium, which occupies about 1/4 in its composition, and other gases. Therefore, despite the fact that the volume of the Sun exceeds the corresponding indicator for the Earth by more than 1.3 million times, the density of this star is still lower than that of our planet. Thus, the density of the Earth is about 5.5 g/cm³, while the density of the Sun is about 1.4 g/cm³: thus, these figures differ by about 4 times.
Newton called mass the amount of matter. Now it is defined as a measure of the inertia of bodies: the heavier the object, the more difficult it is to accelerate it. To find inert mass body, compare the pressure exerted by it on the surface of the support, with the standard, enter the measurement scale. The gravimetric method is used to calculate the mass of celestial bodies.
Instruction
Few people think about how far the star is from us and what size it is. And the numbers are astonishing. Thus, the distance from the Earth to the Sun is 149.6 million kilometers. Moreover, each individual sunbeam reaches the surface of our planet in 8.31 minutes. It is unlikely that in the near future people will learn to fly at the speed of light. Then it would be possible to get to the surface of the star in more than eight minutes.
Sun Dimensions
Everything is relative. If we take our planet and compare it in size with the Sun, it will fit on its surface 109 times. The radius of the star is 695,990 km. At the same time, the mass of the Sun is 333,000 times the mass of the Earth! Moreover, in one second it gives off energy equivalent to 4.26 million tons of mass loss, that is, 3.84x10 to the 26th power of J.
Which of the earthlings can boast that he walked along the equator of the entire planet? Probably, there will be travelers who crossed the Earth on ships and other vehicles. This took a lot of time. It would take them much longer to go around the Sun. It will take at least 109 times more effort and years.
The sun can visually change its size. Sometimes it seems to be several times larger than usual. At other times, on the contrary, it decreases. It all depends on the state of the Earth's atmosphere.
What is the Sun
The sun does not have the same dense mass as most planets. A star can be compared to a spark that constantly gives off heat to the surrounding space. In addition, explosions and plasma separations periodically occur on the surface of the Sun, which greatly affects the well-being of people.
The temperature on the surface of the star is 5770 K, in the center - 15,600,000 K. At an age of 4.57 billion years, the Sun is able to remain the same bright star for a whole time, when compared with human life.
Work N 7. Determination of the angular and linear dimensions of the Sun (or the Moon)
I. With the help of a theodolite.1. After installing the device and inserting a light filter into the eyepiece of the tube, align the zero of the alidade with the zero of the horizontal limb. Fasten the alidade and, with the limb unfastened, point the tube at the Sun so that the vertical thread touches the right edge of the solar disk (this is achieved using the micrometer screw of the limb). Then, by rapidly rotating the micrometer screw of the alidade, move the vertical thread to the left edge of the image of the Sun. Taking readings from the horizontal limb, and get the angular diameter of the Sun.
2. Calculate the radius of the Sun using the formula:
R = D ∙ sinr
where r is the angular radius of the Sun, D is the distance to the Sun.
3. To calculate the linear dimensions of the Sun, you can use another formula. It is known that the radii of the Sun and the Earth are related to the distance to the Sun by the ratio:
R \u003d D ∙ sin r,
R 0 \u003d D ∙ sin p,
where r is the Sun's angular radius and p is its parallax.
Dividing these equalities term by term, we get:
Due to the smallness of the angles, the ratio of sines can be replaced by the ratio of arguments.
Then
The values of parallax p and the radius of the Earth are taken from the tables.
Calculation example.
| R 0 \u003d 6378 km, | 
|
| r=16" | |
| p = 8",8 |
Attitude 
, i.e. the radius of the sun is 109 times the radius of the earth.
The dimensions of the moon are determined in a similar way.
II. According to the time of passage of the disk of the luminary through the vertical filament of the optical tube
If you look at the Sun (or the Moon) through a fixed telescope, then due to the daily rotation of the Earth, the luminary will constantly leave the field of view of the telescope. To determine the angular diameter of the Sun, using a stopwatch, the time it takes for its disk to pass through the vertical thread of the eyepiece is measured and the time found is multiplied by cos d, where d is the declination of the star. Then the time is converted into angular units, remembering that in 1 minute the Earth rotates by 15 "and in 1 second - by 15". The linear diameter D is determined from the ratio:
Where R is the distance to the star, a is its angular diameter, expressed in degrees.
If we use the angular diameter expressed in units of time (for example, in seconds), then 
where t is the time it takes the disk to pass through the vertical thread, expressed in seconds.
Calculation example:
Date of observation - October 28, 1959
The time of passage of the disk through the filament of the eyepiece t = 131 sec.
Sun declination on October 28 d = - 13њ.
The angular diameter of the Sun a = 131∙ cos 13њ = 131∙0.9744 = 128 sec. or in angular units a = 32 = 0.533њ.
Methodical remarks
1. Of the two methods, the second is more accessible. It is simpler in technique and does not require any prior training.
2. When making such measurements, it is interesting to note the difference in the apparent diameter of the Sun when it is at perigee and apogee. This difference is about 1 "or in time - 4 seconds.
The apparent diameter of the Moon varies within much larger limits (from 33.4 to 29.4). This is clearly seen from Fig. 55. There is already a time difference - about 16 seconds.
Rice. 55. The largest and smallest visible dimensions of the disk of the Moon, located concentrically (left) eccentrically (right).
Such observations will convince students with their own eyes that the orbits of the Earth and the Moon are not circular, but elliptical (an illustration of Kepler's laws).
3. Using the second method, you can determine the size of some lunar formations, the length of the shadows from the mountains, etc.
1 The declination is taken from the Astronomical calendar.
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Task 2. Determining the time of maximum and minimum solar activity
Analyze the data in Table 1P, compare the Wolf numbers for 2000–2011 (it is better to do this by building a dependency in EXCEL).
Task 3. Determining the size of sunspots
Determine the angular and linear size of the sunspot (see Fig. A3). Compare the size of this spot with the size of the Earth.
table 2
Task 4. Determining the temperature of the photosphere in the spot area
Examine the bright haloes around sunspots in SOHO images of the Sun's surface. Infer the sunspot temperature, bright halo temperature, and mean photosphere temperature.
Table 3
Make a conclusion about the differences in the image in the photographs and the temperature values.
Task 5. Studying prominences
prominences(German Protuberanzen, from lat. protubero- swell) - dense condensations of relatively cold (compared to the solar corona) matter that rise and are held above the surface of the Sun by a magnetic field.
The following classification of prominences was adopted, taking into account the nature of the motion of matter in them and the form, and was developed at the Crimean Astrophysical Observatory:
Type I (rare) has the form of a cloud or a jet of smoke. Development starts from the foundation; matter rises in a spiral to great heights. The speed of movement of matter can reach 700 km/sec. At an altitude of about 100 thousand km, pieces are separated from the prominence, then falling back along trajectories resembling magnetic field lines;
· II type has the form of curved jets, beginning and ending on the surface of the Sun. Knots and jets move, as it were, along magnetic lines of force. The velocities of bunches are from several tens to 100 km/s. At altitudes of several hundred thousand kilometers, the jets and clumps fade away;
Type III has the shape of a shrub or tree; reaches very large sizes. The motions of bunches (up to tens of km/sec) are disordered.
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| I type | II type | III type |
| Rice. eleven |
Study the prominences from the photographs in Figure 12. Make a conclusion about their size, estimate the approximate temperature. Try to attribute them to one of the three types you know.
Task 6. The study of coronal ejections of the Sun
coronal mass ejections(Coronal mass ejections or CME) are giant volumes of solar matter ejected into interplanetary space from the solar atmosphere as a result of active processes occurring in it. Apparently, it is the substance of coronal ejections that reaches the Earth that is the main cause of the appearance of auroras and magnetic storms.
coronal holes are areas of the corona of the Sun with reduced luminosity. They were discovered after the start of X-ray studies of the Sun using spacecraft from outside the Earth's atmosphere. It is currently believed that the solar wind begins precisely in coronal holes. Coronal holes are low-temperature sources of the solar wind, so they appear dark in images of the Sun.
Task 7. Study of Kreutz comets
Near-solar Comet Kreutz(English) Kreutz Sungrazers) is a family of circumsolar comets named after the German astronomer Heinrich Kreutz (1854–1907), who first showed their relationship. It is believed that they are all parts of one large comet that collapsed several centuries ago.
Kreutz comets can be observed both in the Lasco C2 system and in the Lasco C3 system. Regular observations make it possible to detect new comets and determine their approximate speed.
To determine the speed of comets, a sequence of images is needed with exactly known time of observation of each of them. Then, the coordinates of the comet are determined from the image, and, based on the assumption of their uniform motion, their speed is calculated.
